MIAMI — With the game on the line, the quick-strike New England Patriots showed they can grind out a drive, too.

As a result, they’re the AFC East champions.

Tom Brady had his least efficient game of the season and even threw an interception, but he led a clock-consuming drive in the fourth quarter Sunday that helped the Patriots beat Miami 23-16 to clinch their fourth consecutive division title.

Brady finished 24 for 40 for 238 yards and was sacked four times. But with the Patriots nursing a 20-13 lead midway through the fourth quarter, he led a 16-play drive that took more than seven minutes and led to a field goal.

A botched punt, roughing-the-punter penalty and fumble by Miami resulted in 17 New England points, and another penalty negated a Dolphins touchdown.

The Patriots (9-3) have won six consecutive games and are assured of their 12th winning season in a row. The Dolphins (5-7) hurt their already slim playoff chances and lost to New England for the fifth consecutive time.

Brady was intercepted for the first time in 203 passes, and for only the fourth time this year, and his passer rating was a season-low 74.8. He had at least four passes dropped, including a throw to Wes Welker in the end zone.

The Patriots kept their play-calling conservative and finished with a season-low 321 yards. But when they took over at their 20 leading by a touchdown in the fourth period, they produced their best drive of the day. It covered 77 yards, setting up Stephen Gostkowski’s third field goal with 1:10 to go.

Trevor Scott led New England’s stout defensive effort with two sacks, including one to force a fumble that set up a field goal. Jerod Mayo sacked Ryan Tannehill on third down midway through the fourth quarter, forcing the Dolphins to settle for a field goal.

Welker tied Jerry Rice’s NFL record by making at least 10 catches for the 17th time. He had 12 catches for 103 yards and a score.

Tannehill went only 13 for 29 for 186 yards, but finished two runs with brazen acrobatic leaps. He vaulted over the goal line to elude linebacker Rob Ninkovich on a 2-yard touchdown run.

The botched punt on the Dolphins’ opening series led to a New England touchdown. With the ball wet following a brief shower, punter Brandon Fields dropped a low snap and was tackled at his 12. The Patriots scored five players later on Stevan Ridley’s 2-yard run.

The roughing-the-punter penalty on Miami’s Jimmy Wilson gave the Patriots a first down deep in their territory, jump-starting a 75-yard drive capped by Welker’s 7-yard touchdown catch.

Miami’s Reshad Jones made a one-handed interception and returned the ball 30 yards for a touchdown, but the score was negated by a penalty on Reggie Bush for an illegal block. New England then held, and Dan Carpenter kicked a 44-yard field goal.